Preheat oven to 180C. Turn ice cream machine on to chill, according to manufacturer’s instructions. Set up an ice bath.
For the Coriander Ice Cream, place coriander leaves and milk in the bowl of a small food processor and blitz until coriander is finely chopped and milk is green.
Transfer coriander milk to a saucepan over medium heat, along with cream and vanilla bean and seeds. Bring the mixture to just below boiling point and remove from heat. Set aside to cool slightly.
Meanwhile, place egg yolks and sugar in the bowl of an electric mixer fitted with a whisk attachment and whisk until light and thick. Gradually pour warm milk mixture into the egg mixture, whisking continuously until mixture is smooth.
Return anglaise mixture to the saucepan and cook over medium heat, stirring continuously, until mixture thickens enough to coat the back of a wooden spoon. Transfer the anglaise to a medium bowl and set over an ice bath to cool.
One cold, pour the anglaise into an ice cream machine and churn according to manufacturer’s instructions. Once firm, transfer the ice cream to an airtight container and set aside in freezer until needed.
For the Lime Syrup Cake, place butter and sugar in the bowl of an electric mixer fitted with a paddle attachment and cream until light and fluffy. Add egg and beat well.
Sift in flour and gently fold in to the creamed mixture until combined.
Spoon mixture into 6 x 6.5cm greased dome moulds. Place the moulds on a baking tray and bake in the pre-heated oven for 15 minutes or until golden and cooked through. Remove from oven and allow to cool in moulds for 10 minutes. Once cool, unmould cakes onto a wire cooling rack set over a baking tray and set aside until ready to glaze with Lime Syrup.
Meanwhile, prepare Lime Syrup by combining caster sugar, lime juice and 1/3 cup water in a small saucepan and place over medium heat. Stir frequently until sugar dissolves. Reduce heat slightly and simmer until the mixture has reduced to a syrupy consistency.
Using a wooden skewer or fork, prick several holes into the cakes. Carefully spoon Lime Syrup over the cakes until evenly coated. Set aside until needed.
For the Beetroot Sugar, place beetroot leaves onto a baking tray lined with baking paper and bake in the preheated oven for 10 minutes, or until browned. Set the leaves aside to cool.
When the beetroot leaves are cold, crush finely between your fingers. Place crushed beetroot leaves in a small bowl and mix with remaining ingredients. Set aside until needed.
For the Pickled Stems, chop beetroot and coriander stems into 1cm pieces and set aside in a heatproof bowl. Mix remaining ingredients in a small saucepan and place over medium heat, stirring frequently until sugar has dissolved. Once dissolved strain mixture through a metal sieve. Pour pickling liquid over the stems and set aside to pickle until needed.
For the Beetroot Leaf Chips, place leaves on a baking tray lined with baking paper. Drizzle with oil, season with salt and toss to coat. Bake in the pre-heated oven for 10 minutes, or until crisp. Set aside to cool until needed.
To serve, place a dome cake in centre of each of the serving plates. Rest beetroot crisps on plate. Drain the Pickled Stems and scatter a few of each stem around the plate. Sprinkle a little beetroot sugar around the plate. Serve with quenelle of coriander ice cream.